The table above shows the schedule for the bus routes between three pa

Question

2.jpg The table above shows the schedule for the bus routes between three pairs of cities. If Ash plans to travel by bus from City A, to City B, to City C, and back to City A, what is the shortest possible duration, in minutes, of his entire trip? (A) 120 (B) 130 (C) 140 (D) 150 (E) 160

nick1816 · Answer

Departure times from A are xx:00, xx:20, xx:40

Arrival times at B are xx:25, xx:45, xx:05

Departure times from B are xx:00, xx:30 (minm stay at B = 30-25 = 5 minutes)

Arrival times at C are xx:35, xx:05

Departure times from C are xx:00, xx:20, xx:40 (minm stay at C = 20-05 = 15 minutes, since arrival time is xx:05)

Minm time taken for a round trip = 25+35+60+5+15 = 140

Fdambro294 · Answer

(1st) if there is NO Wait times at city B or City C, the entire trip would take:

25 + 35 + 60 = 120 minutes

(2nd) on top of the 120 minutes of Travel Time, we want to MINIMIZE the Wait Time we spend waiting for the Next Departure in 2 Places:

-1- when we arrive in City B - waiting to Depart City B

and

-2- when we arrive in City C - waiting to Depart City C

Method: usually follow a few Departure Times starting from A and travel through City-to-City, Minimizing the Wait Time for the Next Departure in each Case ------> often, a Pattern will develop

Case 1:
Leave at 5:20 from A

Arrive at 5:45 at B

the Earliest Bus that will leave is at 6:00 ------ (wait 15 minutes)

Arrive at 6:35 at C

the Earliest Bus that will leave is at 6:40 ------ (wait 5 minutes)

Total Travel Times + Total Wait Time = 120 + (15 + 5) = 140 minutes

Eliminate -D- and -E-

Also Eliminate Answer -A- 120 minutes

just looking at the Possible Departures from A (and the fact it takes 25 minutes to get from A-to-B) the MIN wait time in City B will be 5 minutes. Thus, it could never possibly take 120 minutes

Can we get there in less time than 140 minutes?

case 2:
leave A at 5:40

Arrive at B at 6:05

Earliest Bus leaves at 6:30 ------ (25 minute wait time)

Arrive at C at 7:05

Earliest Bus leaves at 7:20 ------ (15 minute wait time)

Total Travel Time + Wait Time = 120 + (25 + 15) = 160 minutes

Case 3:
leave A at 6:00

Arrive at B at 6:25

Earliest Departure is at 6:30 ------ (5 minute wait time)

Arrive at C at 7:05

Earliest Departure is at 7:20 ----- (15 minute wait time)

120 minutes + 20 minutes = 140 minutes

If you keep alternating Departure Times from A every 20 minutes and then MINIMIZE the Time spent waiting for the next departure at Each City,

the Minimum Possible Journey Times will alternate between 140 minutes and 160 minutes

thus, Answer is -C-

140 minutes is the MIN

ScottTargetTestPrep · Answer

Solution:
 
 Scenario 1 : If Ash hops on a bus at 5:00 and leaves City A, he arrives in City B at 5:25. He then hops on a bus at 5:30 and leaves City B and arrives in City C at 6:05. He then hops on a bus at 6:20 and leaves City C and arrives in City A at 7:20. We see that the entire trip lasts 2 hours and 20 minutes, or 140 minutes.

Scenario 2 : If Ash hops on a bus at 5:20 and leaves City A, he arrives in City B at 5:45. He then hops on a bus at 6:00 and leaves City B and arrives in City C at 6:35. He then hops on a bus at 6:40 and leaves City C and arrives in City A at 7:40. We see that the entire trip also lasts 2 hours and 20 minutes, or 140 minutes.

Scenario 3 : If Ash hops on a bus at 5:40 and leaves City A, he arrives in City B at 6:05. He then hops on a bus at 6:30 and leaves City B and arrives in City C at 7:05. He then hops on a bus at 7:20 and leaves City C and arrives in City A at 8:20. We see that the entire trip lasts 2 hours and 40 minutes, or 160 minutes.

If he leaves City A by hopping on a bus at 6:00 or on the hour thereafter, it will be the same as scenario 1. If he hops on a bus at 6:20 or at 20 past the hour thereafter, it will be the same as scenario 2. If he hops on a bus at 6:40 or at 40 past the hour thereafter, it will be the same as scenario 3. Therefore, the shortest possible duration of his entire trip is 140 minutes (scenario 1 or 2)

Answer: C

The table above shows the schedule for the bus routes between three pa

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